Vedic cross-multiplication for two-digit numbers
Unlike most of the tricks in this guide, this one isn't conditional — it works for any two two-digit numbers, not just special cases. The tradeoff is it takes more steps to execute reliably.
The rule
For two numbers "ab" and "cd" (each two digits), compute three pieces:
Middle: (a × d) + (b × c)
Right: b × d
Then combine left, middle and right positionally, carrying into the next position whenever a piece is 10 or more.
Why it works
This is just (10a + b)(10c + d) expanded directly: 100ac + 10ad + 10bc + bd, which regroups into 100(ac) + 10(ad+bc) + bd — the left, middle, and right pieces respectively. Vedic math didn't invent new arithmetic here, it just gives a visual cross pattern for tracking the three products of standard long multiplication without writing out the full grid.
Worked example: 23 × 14
a=2, b=3, c=1, d=4.
Left: 2 × 1 = 2
Middle: (2×4) + (3×1) = 8 + 3 = 11
Right: 3 × 4 = 12
Combine: 2 | 11 | 12 — the middle and right each overflow past one digit, so carry: 12 keeps the 2, carries 1 into the middle → middle becomes 12; 12 keeps the 2, carries 1 into the left → left becomes 3. Result: 322.
Worked example: 34 × 21
a=3, b=4, c=2, d=1.
Left: 3 × 2 = 6
Middle: (3×1) + (4×2) = 3 + 8 = 11
Right: 4 × 1 = 4
Combine: 6 | 11 | 4 — middle overflows, carry 1 into left: left becomes 7, middle becomes 1. Result: 714.
Where this fits in
Because it has no conditions, this is the method to fall back on when none of the more specific shortcuts (×11, base-100, same-tens) apply. It's slower than those in the cases where they do apply, which is why it's worth learning the specific tricks first and treating this as the general-purpose backup.